Department of Mathematical Sciences, University of Texas at El Paso, El Paso, Texas, 79968-0514, USA
Gheorghe Silberberg, Department of Mathematics, University of Timisoara, bd. V. Parvan nr. 4, 1900 Timisoara, ROMANIA
Abstract. The paper studies the structure of the ring A of arithmetical functions, where the multiplication is defined as the Dirichlet convolution. It is proven that A itself is not a discrete valuation ring, but a certain extension of it is constructed,this extension being a discrete valuation ring. Finally, the metric structure of the ring A is examined.
Keywords. Discrete valuation ring, arithmetical function, Dirichlet convolution